[color=#1551b5]Drag point A (in white) to see the orbit of 0 under the Mandelbrot transformation.[/color][br][br][math]z\mapsto z^2+z_A[/math][br][br][math]z_0=0[/math], so [math]z_1=0^2+z_A=z_A[/math], and [math]z_2=z_1^2+z_A[/math] and so on.[br]The different connected points show the successive [math]z_n[/math] of the sequence.[br]The Mandelbrot set (in black) is the set of points A such that this sequence is bounded. [br][br][url]http://prof.pantaloni.free.fr/[/url]

[list][br][*] Check the periodic orbits around the frontier in the numerous bulbs of the Mandelbrot set.[br][*] Observe how a cycle doubles its period when passing from one bulb to a sub-bulb.[br][*] You can assign a specific value to A by typing A=(0.2,0.3) in the input bar.[br][/list]